{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularization\n",
    "\n",
    "Welcome to the second assignment of this week. Deep Learning models have so much flexibility and capacity that **overfitting can be a serious problem**, if the training dataset is not big enough. Sure it does well on the training set, but the learned network **doesn't generalize to new examples** that it has never seen!\n",
    "\n",
    "**You will learn to:** Use regularization in your deep learning models.\n",
    "\n",
    "Let's first import the packages you are going to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:18.943222Z",
     "start_time": "2018-01-20T00:24:18.919938Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import packages\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from reg_utils import sigmoid, relu, plot_decision_boundary, initialize_parameters, load_2D_dataset, predict_dec\n",
    "from reg_utils import compute_cost, predict, forward_propagation, backward_propagation, update_parameters\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "import scipy.io\n",
    "from testCases import *\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Problem Statement**: You have just been hired as an AI expert by the French Football Corporation. They would like you to recommend positions where France's goal keeper should kick the ball so that the French team's players can then hit it with their head. \n",
    "\n",
    "<img src=\"images/field_kiank.png\" style=\"width:600px;height:350px;\">\n",
    "<caption><center> <u> **Figure 1** </u>: **Football field**<br> The goal keeper kicks the ball in the air, the players of each team are fighting to hit the ball with their head </center></caption>\n",
    "\n",
    "\n",
    "They give you the following 2D dataset from France's past 10 games."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:19.173410Z",
     "start_time": "2018-01-20T00:24:18.945408Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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Y6B3nOYpUFJlxk2MZN9m7qv+2jel8fTJde4oDe4/x8t9X8szCC1tUy0BpSjaJT35E7qpE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v2F7P73iqoV+/Guv5sU2mRTuG5bwILbRzftDmlbWmA6ucWgX9xyMTbbGRs/Wk20P78J7c5vHJWY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110400e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_X, train_Y, test_X, test_Y = load_2D_dataset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:19.183701Z",
     "start_time": "2018-01-20T00:24:19.175129Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train_X (2, 211)\n",
      "train_Y (1, 211)\n",
      "test_X (2, 200)\n",
      "test_Y (1, 200)\n",
      "-0.158986\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "print('train_X', train_X.shape)\n",
    "print('train_Y', train_Y.shape)\n",
    "print('test_X', test_X.shape)\n",
    "print('test_Y', test_Y.shape)\n",
    "print(train_X[0, 0])\n",
    "print(train_Y[0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each dot corresponds to a position on the football field where a football player has hit the ball with his/her head after the French goal keeper has shot the ball from the left side of the football field.\n",
    "- If the dot is blue, it means the French player managed to hit the ball with his/her head\n",
    "- If the dot is red, it means the other team's player hit the ball with their head\n",
    "\n",
    "**Your goal**: Use a deep learning model to find the positions on the field where the goalkeeper should kick the ball."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Analysis of the dataset**: This dataset is a little noisy, but it looks like a diagonal line separating the upper left half (blue) from the lower right half (red) would work well. \n",
    "\n",
    "You will first try a non-regularized model. Then you'll learn how to regularize it and decide which model you will choose to solve the French Football Corporation's problem. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Non-regularized model\n",
    "\n",
    "You will use the following neural network (already implemented for you below). This model can be used:\n",
    "- in *regularization mode* -- by setting the `lambd` input to a non-zero value. We use \"`lambd`\" instead of \"`lambda`\" because \"`lambda`\" is a reserved keyword in Python. \n",
    "- in *dropout mode* -- by setting the `keep_prob` to a value less than one\n",
    "\n",
    "You will first try the model without any regularization. Then, you will implement:\n",
    "- *L2 regularization* -- functions: \"`compute_cost_with_regularization()`\" and \"`backward_propagation_with_regularization()`\"\n",
    "- *Dropout* -- functions: \"`forward_propagation_with_dropout()`\" and \"`backward_propagation_with_dropout()`\"\n",
    "\n",
    "In each part, you will run this model with the correct inputs so that it calls the functions you've implemented. Take a look at the code below to familiarize yourself with the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:19.190862Z",
     "start_time": "2018-01-20T00:24:19.186935Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# forward_propagation??\n",
    "# backward_propagation??\n",
    "# compute_cost??\n",
    "# update_parameters??\n",
    "# predict??\n",
    "# initialize_parameters??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:19.240645Z",
     "start_time": "2018-01-20T00:24:19.193029Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X, Y, learning_rate = 0.3, num_iterations = 30000, print_cost = True, lambd = 0, keep_prob = 1):\n",
    "    \"\"\"\n",
    "    Implements a three-layer neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SIGMOID.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (input size, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (output size, number of examples)\n",
    "    learning_rate -- learning rate of the optimization\n",
    "    num_iterations -- number of iterations of the optimization loop\n",
    "    print_cost -- If True, print the cost every 10000 iterations\n",
    "    lambd -- regularization hyperparameter, scalar\n",
    "    keep_prob - probability of keeping a neuron active during drop-out, scalar.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- parameters learned by the model. They can then be used to predict.\n",
    "    \"\"\"\n",
    "        \n",
    "    grads = {}\n",
    "    costs = []                            # to keep track of the cost\n",
    "    m = X.shape[1]                        # number of examples\n",
    "    layers_dims = [X.shape[0], 20, 3, 1]\n",
    "    \n",
    "    # Initialize parameters dictionary.\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Loop (gradient descent)\n",
    "\n",
    "    for i in range(0, num_iterations):\n",
    "\n",
    "        # Forward propagation: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID.\n",
    "        if keep_prob == 1:\n",
    "            a3, cache = forward_propagation(X, parameters)\n",
    "        elif keep_prob < 1:\n",
    "            a3, cache = forward_propagation_with_dropout(X, parameters, keep_prob)\n",
    "        \n",
    "        # Cost function\n",
    "        if lambd == 0:\n",
    "            cost = compute_cost(a3, Y)\n",
    "        else:\n",
    "            cost = compute_cost_with_regularization(a3, Y, parameters, lambd)\n",
    "            \n",
    "        # Backward propagation.\n",
    "        assert(lambd==0 or keep_prob==1)    # it is possible to use both L2 regularization and dropout, \n",
    "                                            # but this assignment will only explore one at a time\n",
    "        if lambd == 0 and keep_prob == 1:\n",
    "            grads = backward_propagation(X, Y, cache)\n",
    "        elif lambd != 0:\n",
    "            grads = backward_propagation_with_regularization(X, Y, cache, lambd)\n",
    "        elif keep_prob < 1:\n",
    "            grads = backward_propagation_with_dropout(X, Y, cache, keep_prob)\n",
    "        \n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads, learning_rate)\n",
    "        \n",
    "        # Print the loss every 10000 iterations\n",
    "        if print_cost and i % 10000 == 0:\n",
    "            print(\"Cost after iteration {}: {}\".format(i, cost))\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            costs.append(cost)\n",
    "    \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('iterations (x1,000)')\n",
    "    plt.title(\"Learning rate =\" + str(learning_rate))\n",
    "    plt.show()\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's train the model without any regularization, and observe the accuracy on the train/test sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:26.292086Z",
     "start_time": "2018-01-20T00:24:19.242748Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.6557412523481002\n",
      "Cost after iteration 10000: 0.16329987525724213\n",
      "Cost after iteration 20000: 0.1385164242325169\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1106906a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "On the training set:\n",
      "Accuracy: 0.947867298578\n",
      "On the test set:\n",
      "Accuracy: 0.915\n"
     ]
    }
   ],
   "source": [
    "parameters = model(train_X, train_Y)\n",
    "# print(parameters)\n",
    "print (\"On the training set:\")\n",
    "predictions_train = predict(train_X, train_Y, parameters)\n",
    "print (\"On the test set:\")\n",
    "predictions_test = predict(test_X, test_Y, parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The train accuracy is 94.8% while the test accuracy is 91.5%. This is the **baseline model** (you will observe the impact of regularization on this model). Run the following code to plot the decision boundary of your model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:49.461270Z",
     "start_time": "2018-01-20T00:24:49.455183Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# predict_dec??\n",
    "# plot_decision_boundary??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:50.107236Z",
     "start_time": "2018-01-20T00:24:49.669615Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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E9uFkw617HBZOLc/ZLC272Kelm2uYGcZQGh4L3E5AtuHFWbGl1Ewl1byMM9oQ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nAAAC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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1109ef400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Model without regularization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-0.75,0.40])\n",
    "axes.set_ylim([-0.75,0.65])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The non-regularized model is obviously overfitting the training set. It is fitting the noisy points! Lets now look at two techniques to reduce overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - L2 Regularization\n",
    "\n",
    "The standard way to avoid overfitting is called **L2 regularization**. It consists of appropriately modifying your cost function, from:\n",
    "$$J = -\\frac{1}{m} \\sum\\limits_{i = 1}^{m} \\large{(}\\small  y^{(i)}\\log\\left(a^{[L](i)}\\right) + (1-y^{(i)})\\log\\left(1- a^{[L](i)}\\right) \\large{)} \\tag{1}$$\n",
    "To:\n",
    "$$J_{regularized} = \\small \\underbrace{-\\frac{1}{m} \\sum\\limits_{i = 1}^{m} \\large{(}\\small y^{(i)}\\log\\left(a^{[L](i)}\\right) + (1-y^{(i)})\\log\\left(1- a^{[L](i)}\\right) \\large{)} }_\\text{cross-entropy cost} + \\underbrace{\\frac{1}{m} \\frac{\\lambda}{2} \\sum\\limits_l\\sum\\limits_k\\sum\\limits_j W_{k,j}^{[l]2} }_\\text{L2 regularization cost} \\tag{2}$$\n",
    "\n",
    "Let's modify your cost and observe the consequences.\n",
    "\n",
    "**Exercise**: Implement `compute_cost_with_regularization()` which computes the cost given by formula (2). To calculate $\\sum\\limits_k\\sum\\limits_j W_{k,j}^{[l]2}$  , use :\n",
    "```python\n",
    "np.sum(np.square(Wl))\n",
    "```\n",
    "Note that you have to do this for $W^{[1]}$, $W^{[2]}$ and $W^{[3]}$, then sum the three terms and multiply by $ \\frac{1}{m} \\frac{\\lambda}{2} $."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:51.124247Z",
     "start_time": "2018-01-20T00:24:51.119378Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# print(np.info(np.square))\n",
    "# compute_cost??\n",
    "# print(np.info(np.nansum))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:51.532443Z",
     "start_time": "2018-01-20T00:24:51.520972Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: compute_cost_with_regularization\n",
    "\n",
    "def compute_cost_with_regularization(A3, Y, parameters, lambd):\n",
    "    \"\"\"\n",
    "    Implement the cost function with L2 regularization. See formula (2) above.\n",
    "    \n",
    "    Arguments:\n",
    "    A3 -- post-activation, output of forward propagation, of shape (output size, number of examples)\n",
    "    Y -- \"true\" labels vector, of shape (output size, number of examples)\n",
    "    parameters -- python dictionary containing parameters of the model\n",
    "    \n",
    "    Returns:\n",
    "    cost - value of the regularized loss function (formula (2))\n",
    "    \"\"\"\n",
    "    m = Y.shape[1]\n",
    "    W1 = parameters[\"W1\"]\n",
    "    W2 = parameters[\"W2\"]\n",
    "    W3 = parameters[\"W3\"]\n",
    "    \n",
    "    cross_entropy_cost = compute_cost(A3, Y) # This gives you the cross-entropy part of the cost\n",
    "    \n",
    "    ### START CODE HERE ### (approx. 1 line)\n",
    "    L2_regularization_cost = 1 / m * lambd / 2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)) + np.sum(np.square(W3)))\n",
    "    ### END CODER HERE ###\n",
    "    \n",
    "    cost = cross_entropy_cost + L2_regularization_cost\n",
    "    \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:52.434148Z",
     "start_time": "2018-01-20T00:24:52.427253Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cost = 1.78648594516\n"
     ]
    }
   ],
   "source": [
    "A3, Y_assess, parameters = compute_cost_with_regularization_test_case()\n",
    "\n",
    "print(\"cost = \" + str(compute_cost_with_regularization(A3, Y_assess, parameters, lambd = 0.1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td>\n",
    "    **cost**\n",
    "    </td>\n",
    "        <td>\n",
    "    1.78648594516\n",
    "    </td>\n",
    "    \n",
    "    </tr>\n",
    "\n",
    "</table> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, because you changed the cost, you have to change backward propagation as well! All the gradients have to be computed with respect to this new cost. \n",
    "\n",
    "**Exercise**: Implement the changes needed in backward propagation to take into account regularization. The changes only concern dW1, dW2 and dW3. For each, you have to add the regularization term's gradient ($\\frac{d}{dW} ( \\frac{1}{2}\\frac{\\lambda}{m}  W^2) = \\frac{\\lambda}{m} W$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:54.738522Z",
     "start_time": "2018-01-20T00:24:54.702560Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: backward_propagation_with_regularization\n",
    "\n",
    "def backward_propagation_with_regularization(X, Y, cache, lambd):\n",
    "    \"\"\"\n",
    "    Implements the backward propagation of our baseline model to which we added an L2 regularization.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input dataset, of shape (input size, number of examples)\n",
    "    Y -- \"true\" labels vector, of shape (output size, number of examples)\n",
    "    cache -- cache output from forward_propagation()\n",
    "    lambd -- regularization hyperparameter, scalar\n",
    "    \n",
    "    Returns:\n",
    "    gradients -- A dictionary with the gradients with respect to each parameter, activation and pre-activation variables\n",
    "    \"\"\"\n",
    "    \n",
    "    m = X.shape[1]\n",
    "    (Z1, A1, W1, b1, Z2, A2, W2, b2, Z3, A3, W3, b3) = cache\n",
    "    \n",
    "    dZ3 = A3 - Y\n",
    "    \n",
    "    ### START CODE HERE ### (approx. 1 line)\n",
    "    dW3 = 1./m * np.dot(dZ3, A2.T) + lambd / m * W3\n",
    "    ### END CODE HERE ###\n",
    "    db3 = 1./m * np.sum(dZ3, axis=1, keepdims = True)\n",
    "    \n",
    "    dA2 = np.dot(W3.T, dZ3)\n",
    "    dZ2 = np.multiply(dA2, np.int64(A2 > 0))\n",
    "    ### START CODE HERE ### (approx. 1 line)\n",
    "    dW2 = 1./m * np.dot(dZ2, A1.T) + lambd / m * W2\n",
    "    ### END CODE HERE ###\n",
    "    db2 = 1./m * np.sum(dZ2, axis=1, keepdims = True)\n",
    "    \n",
    "    dA1 = np.dot(W2.T, dZ2)\n",
    "    dZ1 = np.multiply(dA1, np.int64(A1 > 0))\n",
    "    ### START CODE HERE ### (approx. 1 line)\n",
    "    dW1 = 1./m * np.dot(dZ1, X.T) + lambd / m * W1\n",
    "    ### END CODE HERE ###\n",
    "    db1 = 1./m * np.sum(dZ1, axis=1, keepdims = True)\n",
    "    \n",
    "    gradients = {\"dZ3\": dZ3, \"dW3\": dW3, \"db3\": db3,\"dA2\": dA2,\n",
    "                 \"dZ2\": dZ2, \"dW2\": dW2, \"db2\": db2, \"dA1\": dA1, \n",
    "                 \"dZ1\": dZ1, \"dW1\": dW1, \"db1\": db1}\n",
    "    \n",
    "    return gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:24:55.506949Z",
     "start_time": "2018-01-20T00:24:55.495410Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dW1 = [[-0.25604646  0.12298827 -0.28297129]\n",
      " [-0.17706303  0.34536094 -0.4410571 ]]\n",
      "dW2 = [[ 0.79276486  0.85133918]\n",
      " [-0.0957219  -0.01720463]\n",
      " [-0.13100772 -0.03750433]]\n",
      "dW3 = [[-1.77691347 -0.11832879 -0.09397446]]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess, cache = backward_propagation_with_regularization_test_case()\n",
    "\n",
    "grads = backward_propagation_with_regularization(X_assess, Y_assess, cache, lambd = 0.7)\n",
    "print (\"dW1 = \"+ str(grads[\"dW1\"]))\n",
    "print (\"dW2 = \"+ str(grads[\"dW2\"]))\n",
    "print (\"dW3 = \"+ str(grads[\"dW3\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td>\n",
    "    **dW1**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[-0.25604646  0.12298827 -0.28297129]\n",
    " [-0.17706303  0.34536094 -0.4410571 ]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **dW2**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.79276486  0.85133918]\n",
    " [-0.0957219  -0.01720463]\n",
    " [-0.13100772 -0.03750433]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **dW3**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[-1.77691347 -0.11832879 -0.09397446]]\n",
    "    </td>\n",
    "    </tr>\n",
    "</table> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now run the model with L2 regularization $(\\lambda = 0.7)$. The `model()` function will call: \n",
    "- `compute_cost_with_regularization` instead of `compute_cost`\n",
    "- `backward_propagation_with_regularization` instead of `backward_propagation`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:25:04.012882Z",
     "start_time": "2018-01-20T00:24:57.262373Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.6974484493131264\n",
      "Cost after iteration 10000: 0.2684918873282239\n",
      "Cost after iteration 20000: 0.2680916337127301\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f6cfa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "On the train set:\n",
      "Accuracy: 0.938388625592\n",
      "On the test set:\n",
      "Accuracy: 0.93\n"
     ]
    }
   ],
   "source": [
    "parameters = model(train_X, train_Y, lambd = 0.7)\n",
    "print (\"On the train set:\")\n",
    "predictions_train = predict(train_X, train_Y, parameters)\n",
    "print (\"On the test set:\")\n",
    "predictions_test = predict(test_X, test_Y, parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Congrats, the test set accuracy increased to 93%. You have saved the French football team!\n",
    "\n",
    "You are not overfitting the training data anymore. Let's plot the decision boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:25:06.314417Z",
     "start_time": "2018-01-20T00:25:06.058132Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7rHRzDVPDGErDI4HbCkjXvDgrtpCYqqSal3KGGwIhbj48Jhs3C8w/qJFqdATd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\naKHUaDQajaYLWig1Go1Go+nC/w93O6WMf7YPywAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10326aac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Model with L2-regularization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-0.75,0.40])\n",
    "axes.set_ylim([-0.75,0.65])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Observations**:\n",
    "- The value of $\\lambda$ is a hyperparameter that you can tune using a dev set.\n",
    "- L2 regularization makes your decision boundary smoother. If $\\lambda$ is too large, it is also possible to \"oversmooth\", resulting in a model with high bias.\n",
    "\n",
    "**What is L2-regularization actually doing?**:\n",
    "\n",
    "L2-regularization relies on the assumption that a model with small weights is simpler than a model with large weights. Thus, by penalizing the square values of the weights in the cost function you drive all the weights to smaller values. It becomes too costly for the cost to have large weights! This leads to a smoother model in which the output changes more slowly as the input changes. \n",
    "\n",
    "<font color='blue'>\n",
    "**What you should remember** -- the implications of L2-regularization on:\n",
    "- The cost computation:\n",
    "    - A regularization term is added to the cost\n",
    "- The backpropagation function:\n",
    "    - There are extra terms in the gradients with respect to weight matrices\n",
    "- Weights end up smaller (\"weight decay\"): \n",
    "    - Weights are pushed to smaller values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Dropout\n",
    "\n",
    "Finally, **dropout** is a widely used regularization technique that is specific to deep learning. \n",
    "**It randomly shuts down some neurons in each iteration.** Watch these two videos to see what this means!\n",
    "\n",
    "<!--\n",
    "To understand drop-out, consider this conversation with a friend:\n",
    "- Friend: \"Why do you need all these neurons to train your network and classify images?\". \n",
    "- You: \"Because each neuron contains a weight and can learn specific features/details/shape of an image. The more neurons I have, the more featurse my model learns!\"\n",
    "- Friend: \"I see, but are you sure that your neurons are learning different features and not all the same features?\"\n",
    "- You: \"Good point... Neurons in the same layer actually don't talk to each other. It should be definitly possible that they learn the same image features/shapes/forms/details... which would be redundant. There should be a solution.\"\n",
    "!--> \n",
    "\n",
    "\n",
    "<center>\n",
    "<video width=\"620\" height=\"440\" src=\"images/dropout1_kiank.mp4\" type=\"video/mp4\" controls>\n",
    "</video>\n",
    "</center>\n",
    "<br>\n",
    "<caption><center> <u> Figure 2 </u>: Drop-out on the second hidden layer. <br> At each iteration, you shut down (= set to zero) each neuron of a layer with probability $1 - keep\\_prob$ or keep it with probability $keep\\_prob$ (50% here). The dropped neurons don't contribute to the training in both the forward and backward propagations of the iteration. </center></caption>\n",
    "\n",
    "<center>\n",
    "<video width=\"620\" height=\"440\" src=\"images/dropout2_kiank.mp4\" type=\"video/mp4\" controls>\n",
    "</video>\n",
    "</center>\n",
    "\n",
    "<caption><center> <u> Figure 3 </u>: Drop-out on the first and third hidden layers. <br> $1^{st}$ layer: we shut down on average 40% of the neurons.  $3^{rd}$ layer: we shut down on average 20% of the neurons. </center></caption>\n",
    "\n",
    "\n",
    "When you shut some neurons down, you actually modify your model. The idea behind drop-out is that at each iteration, you train a different model that uses only a subset of your neurons. With dropout, your neurons thus become less sensitive to the activation of one other specific neuron, because that other neuron might be shut down at any time. \n",
    "\n",
    "### 3.1 - Forward propagation with dropout\n",
    "\n",
    "**Exercise**: Implement the forward propagation with dropout. You are using a 3 layer neural network, and will add dropout to the first and second hidden layers. We will not apply dropout to the input layer or output layer. \n",
    "\n",
    "**Instructions**:\n",
    "You would like to shut down some neurons in the first and second layers. To do that, you are going to carry out 4 Steps:\n",
    "1. In lecture, we dicussed creating a variable $d^{[1]}$ with the same shape as $a^{[1]}$ using `np.random.rand()` to randomly get numbers between 0 and 1. Here, you will use a vectorized implementation, so create a random matrix $D^{[1]} = [d^{[1](1)} d^{[1](2)} ... d^{[1](m)}] $ of the same dimension as $A^{[1]}$.\n",
    "2. Set each entry of $D^{[1]}$ to be 0 with probability (`1-keep_prob`) or 1 with probability (`keep_prob`), by thresholding values in $D^{[1]}$ appropriately. Hint: to set all the entries of a matrix X to 0 (if entry is less than 0.5) or 1 (if entry is more than 0.5) you would do: `X = (X < 0.5)`. Note that 0 and 1 are respectively equivalent to False and True.\n",
    "3. Set $A^{[1]}$ to $A^{[1]} * D^{[1]}$. (You are shutting down some neurons). You can think of $D^{[1]}$ as a mask, so that when it is multiplied with another matrix, it shuts down some of the values.\n",
    "4. Divide $A^{[1]}$ by `keep_prob`. By doing this you are assuring that the result of the cost will still have the same expected value as without drop-out. (This technique is also called inverted dropout.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:30:38.974898Z",
     "start_time": "2018-01-20T00:30:38.940480Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: forward_propagation_with_dropout\n",
    "\n",
    "def forward_propagation_with_dropout(X, parameters, keep_prob = 0.5):\n",
    "    \"\"\"\n",
    "    Implements the forward propagation: LINEAR -> RELU + DROPOUT -> LINEAR -> RELU + DROPOUT -> LINEAR -> SIGMOID.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input dataset, of shape (2, number of examples)\n",
    "    parameters -- python dictionary containing your parameters \"W1\", \"b1\", \"W2\", \"b2\", \"W3\", \"b3\":\n",
    "                    W1 -- weight matrix of shape (20, 2)\n",
    "                    b1 -- bias vector of shape (20, 1)\n",
    "                    W2 -- weight matrix of shape (3, 20)\n",
    "                    b2 -- bias vector of shape (3, 1)\n",
    "                    W3 -- weight matrix of shape (1, 3)\n",
    "                    b3 -- bias vector of shape (1, 1)\n",
    "    keep_prob - probability of keeping a neuron active during drop-out, scalar\n",
    "    \n",
    "    Returns:\n",
    "    A3 -- last activation value, output of the forward propagation, of shape (1,1)\n",
    "    cache -- tuple, information stored for computing the backward propagation\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(1)\n",
    "    \n",
    "    # retrieve parameters\n",
    "    W1 = parameters[\"W1\"]\n",
    "    b1 = parameters[\"b1\"]\n",
    "    W2 = parameters[\"W2\"]\n",
    "    b2 = parameters[\"b2\"]\n",
    "    W3 = parameters[\"W3\"]\n",
    "    b3 = parameters[\"b3\"]\n",
    "    \n",
    "    # LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID\n",
    "    Z1 = np.dot(W1, X) + b1\n",
    "    A1 = relu(Z1)\n",
    "#     print(A1.shape)\n",
    "    ### START CODE HERE ### (approx. 4 lines)         # Steps 1-4 below correspond to the Steps 1-4 described above. \n",
    "    D1 = np.random.rand(*A1.shape)         # Step 1: initialize matrix D1 = np.random.rand(..., ...)\n",
    "    D1 = (D1 <= keep_prob)                                         # Step 2: convert entries of D1 to 0 or 1 (using keep_prob as the threshold)\n",
    "    A1 = A1 * D1                                         # Step 3: shut down some neurons of A1\n",
    "    A1 = A1 / keep_prob                                         # Step 4: scale the value of neurons that haven't been shut down\n",
    "    ### END CODE HERE ###\n",
    "    Z2 = np.dot(W2, A1) + b2\n",
    "    A2 = relu(Z2)\n",
    "    ### START CODE HERE ### (approx. 4 lines)\n",
    "    D2 = np.random.rand(*A2.shape)                                          # Step 1: initialize matrix D2 = np.random.rand(..., ...)\n",
    "    D2 = (D2 <= keep_prob)                                             # Step 2: convert entries of D2 to 0 or 1 (using keep_prob as the threshold)\n",
    "    A2 = A2 * D2                                          # Step 3: shut down some neurons of A2\n",
    "    A2 = A2 / keep_prob                                           # Step 4: scale the value of neurons that haven't been shut down\n",
    "    ### END CODE HERE ###\n",
    "    Z3 = np.dot(W3, A2) + b3\n",
    "    A3 = sigmoid(Z3)\n",
    "    \n",
    "    cache = (Z1, D1, A1, W1, b1, Z2, D2, A2, W2, b2, Z3, A3, W3, b3)\n",
    "    \n",
    "    return A3, cache"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:30:42.468100Z",
     "start_time": "2018-01-20T00:30:42.462800Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A3 = [[ 0.36974721  0.00305176  0.04565099  0.49683389  0.36974721]]\n"
     ]
    }
   ],
   "source": [
    "X_assess, parameters = forward_propagation_with_dropout_test_case()\n",
    "\n",
    "A3, cache = forward_propagation_with_dropout(X_assess, parameters, keep_prob = 0.7)\n",
    "print (\"A3 = \" + str(A3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td>\n",
    "    **A3**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.36974721  0.00305176  0.04565099  0.49683389  0.36974721]]\n",
    "    </td>\n",
    "    \n",
    "    </tr>\n",
    "\n",
    "</table> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 - Backward propagation with dropout\n",
    "\n",
    "**Exercise**: Implement the backward propagation with dropout. As before, you are training a 3 layer network. Add dropout to the first and second hidden layers, using the masks $D^{[1]}$ and $D^{[2]}$ stored in the cache. \n",
    "\n",
    "**Instruction**:\n",
    "Backpropagation with dropout is actually quite easy. You will have to carry out 2 Steps:\n",
    "1. You had previously shut down some neurons during forward propagation, by applying a mask $D^{[1]}$ to `A1`. In backpropagation, you will have to shut down the same neurons, by reapplying the same mask $D^{[1]}$ to `dA1`. \n",
    "2. During forward propagation, you had divided `A1` by `keep_prob`. In backpropagation, you'll therefore have to divide `dA1` by `keep_prob` again (the calculus interpretation is that if $A^{[1]}$ is scaled by `keep_prob`, then its derivative $dA^{[1]}$ is also scaled by the same `keep_prob`).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:32:38.897973Z",
     "start_time": "2018-01-20T00:32:38.857819Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: backward_propagation_with_dropout\n",
    "\n",
    "def backward_propagation_with_dropout(X, Y, cache, keep_prob):\n",
    "    \"\"\"\n",
    "    Implements the backward propagation of our baseline model to which we added dropout.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input dataset, of shape (2, number of examples)\n",
    "    Y -- \"true\" labels vector, of shape (output size, number of examples)\n",
    "    cache -- cache output from forward_propagation_with_dropout()\n",
    "    keep_prob - probability of keeping a neuron active during drop-out, scalar\n",
    "    \n",
    "    Returns:\n",
    "    gradients -- A dictionary with the gradients with respect to each parameter, activation and pre-activation variables\n",
    "    \"\"\"\n",
    "    \n",
    "    m = X.shape[1]\n",
    "    (Z1, D1, A1, W1, b1, Z2, D2, A2, W2, b2, Z3, A3, W3, b3) = cache\n",
    "    \n",
    "    dZ3 = A3 - Y\n",
    "    dW3 = 1./m * np.dot(dZ3, A2.T)\n",
    "    db3 = 1./m * np.sum(dZ3, axis=1, keepdims = True)\n",
    "    dA2 = np.dot(W3.T, dZ3)\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    dA2 = dA2 * D2              # Step 1: Apply mask D2 to shut down the same neurons as during the forward propagation\n",
    "    dA2 = dA2 / keep_prob              # Step 2: Scale the value of neurons that haven't been shut down\n",
    "    ### END CODE HERE ###\n",
    "    dZ2 = np.multiply(dA2, np.int64(A2 > 0))\n",
    "    dW2 = 1./m * np.dot(dZ2, A1.T)\n",
    "    db2 = 1./m * np.sum(dZ2, axis=1, keepdims = True)\n",
    "    \n",
    "    dA1 = np.dot(W2.T, dZ2)\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    dA1 = dA1 * D1                  # Step 1: Apply mask D1 to shut down the same neurons as during the forward propagation\n",
    "    dA1 = dA1 / keep_prob               # Step 2: Scale the value of neurons that haven't been shut down\n",
    "    ### END CODE HERE ###\n",
    "    dZ1 = np.multiply(dA1, np.int64(A1 > 0))\n",
    "    dW1 = 1./m * np.dot(dZ1, X.T)\n",
    "    db1 = 1./m * np.sum(dZ1, axis=1, keepdims = True)\n",
    "    \n",
    "    gradients = {\"dZ3\": dZ3, \"dW3\": dW3, \"db3\": db3,\"dA2\": dA2,\n",
    "                 \"dZ2\": dZ2, \"dW2\": dW2, \"db2\": db2, \"dA1\": dA1, \n",
    "                 \"dZ1\": dZ1, \"dW1\": dW1, \"db1\": db1}\n",
    "    \n",
    "    return gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:38:13.681560Z",
     "start_time": "2018-01-20T00:38:13.669438Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dA1 = [[ 0.36544439  0.         -0.00188233  0.         -0.17408748]\n",
      " [ 0.65515713  0.         -0.00337459  0.         -0.        ]]\n",
      "db1 = [[-0.00037647]\n",
      " [-0.00067492]]\n",
      "dA2 = [[ 0.58180856  0.         -0.00299679  0.         -0.27715731]\n",
      " [ 0.          0.53159854 -0.          0.53159854 -0.34089673]\n",
      " [ 0.          0.         -0.00292733  0.         -0.        ]]\n",
      "db2 = [[ 0.06033089]\n",
      " [ 0.        ]\n",
      " [ 0.        ]]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess, cache = backward_propagation_with_dropout_test_case()\n",
    "\n",
    "gradients = backward_propagation_with_dropout(X_assess, Y_assess, cache, keep_prob = 0.8)\n",
    "\n",
    "print (\"dA1 = \" + str(gradients[\"dA1\"]))\n",
    "print (\"db1 = \" + str(gradients[\"db1\"]))\n",
    "print (\"dA2 = \" + str(gradients[\"dA2\"]))\n",
    "print (\"db2 = \" + str(gradients[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td>\n",
    "    **dA1**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.36544439  0.         -0.00188233  0.         -0.17408748]\n",
    " [ 0.65515713  0.         -0.00337459  0.         -0.        ]]\n",
    "    </td>\n",
    "    \n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **dA2**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.58180856  0.         -0.00299679  0.         -0.27715731]\n",
    " [ 0.          0.53159854 -0.          0.53159854 -0.34089673]\n",
    " [ 0.          0.         -0.00292733  0.         -0.        ]]\n",
    "    </td>\n",
    "    \n",
    "    </tr>\n",
    "</table> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now run the model with dropout (`keep_prob = 0.86`). It means at every iteration you shut down each neurons of layer 1 and 2 with 24% probability. The function `model()` will now call:\n",
    "- `forward_propagation_with_dropout` instead of `forward_propagation`.\n",
    "- `backward_propagation_with_dropout` instead of `backward_propagation`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:33:13.316507Z",
     "start_time": "2018-01-20T00:33:04.140672Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.6543912405149825\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/thomas_young/Documents/doc/deepLearning/coursera_deep_learning/深度学习第二课作业/week5/Regularization/reg_utils.py:236: RuntimeWarning: divide by zero encountered in log\n",
      "  logprobs = np.multiply(-np.log(a3),Y) + np.multiply(-np.log(1 - a3), 1 - Y)\n",
      "/Users/thomas_young/Documents/doc/deepLearning/coursera_deep_learning/深度学习第二课作业/week5/Regularization/reg_utils.py:236: RuntimeWarning: invalid value encountered in multiply\n",
      "  logprobs = np.multiply(-np.log(a3),Y) + np.multiply(-np.log(1 - a3), 1 - Y)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 10000: 0.061016986574905605\n",
      "Cost after iteration 20000: 0.060582435798513114\n"
     ]
    },
    {
     "data": {
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demZmheLQ64GbTpuZFZNDrwduOm1mVky5hp6kGZIWSVos6fweHp8paYGk+yR1SDohz3rq\n5abTZmbFlNt37SQ1A5cAbwM6gfmS5lac9XkTMDciQtKRwK+Bw/KqaVe46bSZWfHkOdKbDiyOiCUR\nsRm4EpiZXSAi1kdEpJPDgGAP4abTZmbFk2fojQeWZqY703kvI+k0SY8AvyPp6fl3JM1Od392dHV1\n5VJsJTedNjMrnoafyBIR10TEYcA7gC9XWeayiJgWEdPa2wfmMn5uOm1mVjx5ht4yYGJmekI6r0cR\ncQtwkKRxOdZUNzedNjMrnjxDbz4wVdIUSW3ALGBudgFJh0hSev8YYBB7yMVp3XTazKx4cjt7MyK2\nSpoD3AA0A5dHxEJJ56WPXwq8Ezhb0hZgI/DuzIktDeWm02ZmxZPr5YEiYh4wr2LepZn7XwW+mmcN\nfeWm02ZmxdPwE1n2VG46bWZWPA69Ktx02syseBx6VbjptJlZ8Tj0quhuOr3KX1A3MysMh14V3U2n\n/QV1M7PicOjV4KbTZmbF4tCrYczQNu/eNDMrEIdeDWOGtvpEFjOzAnHo1eCm02ZmxeLQq2Hs0DZ/\nOd3MrEAcejWMGdbGi246bWZWGA69GrJNp83MbO/n0Ksh23TazMz2fg69Gtx02sysWBx6NbjptJlZ\nsTj0anDTaTOzYnHo1eCm02ZmxeLQq8FNp83MisWh1ws3nTYzKw6HXi/cdNrMrDgcer1w02kzs+Jw\n6PXCTafNzIrDodcLN502MysOh14v3HTazKw4cg09STMkLZK0WNL5PTz+XkkLJD0g6XZJR+VZT1+4\n6bSZWXHkFnqSmoFLgJOBw4H3SDq8YrEngDdHxKuBLwOX5VVPX3U3nfbXFszM9n55jvSmA4sjYklE\nbAauBGZmF4iI2yNiVTp5JzAhx3r6xK3IzMyKI8/QGw8szUx3pvOq+SDw+54ekDRbUoekjq6urn4s\nsXduOm1mVhx7xIkskk4iCb3P9vR4RFwWEdMiYlp7e/uA1rZjpOdjemZme72WHNe9DJiYmZ6QznsZ\nSUcCPwJOjogVOdbTJzuaTnv3ppnZXi/Pkd58YKqkKZLagFnA3OwCkiYBVwPvj4hHc6ylz9x02sys\nOHIb6UXEVklzgBuAZuDyiFgo6bz08UuBzwP7AN+TBLA1IqblVVNfuem0mVkx5Ll7k4iYB8yrmHdp\n5v6HgA/lWUN/cNNpM7Ni2CNOZNnTuem0mVkxOPTq4KbTZmbF4NCrw34jB7N83SaWr9vU6FLMzGw3\nOPTq8O5pE9ke8P0/P97oUszMbDc49OowedwwzjhmAj+/62meXbOx0eWYmVkfOfTqNOcthxARXHLz\n4kaXYmZmfeTQq9PEsUM5c9pEfjV/KZ2rNjS6HDMz6wOH3i6Y85ZDkMS/3+TRnpnZ3sihtwsOGDWE\ns6ZP4rf3dvLUihcbXY6Zme0ih94u+uhJB9PaLL5z02ONLsXMzHaRQ28X7TtiMGcfP5lr/7aMxcvX\nN7ocMzPbBQ69Pvjwmw5icGuzR3tmZnsZh14f7DN8EOe+fjLXL3iGRc+ta3Q5ZmZWJ4deH81+00EM\nb2vh23/aIy8DaGZmPXDo9dHooW184IQp/P7B51j4zJpGl2NmZnVw6O2GD75xCiMHt/CtGz3aMzPb\nGzj0dsPIwa3MftNB/Onh5dy3dHWjyzEzs1449HbTuW+YwpihrVzk0Z6Z2R7Pobebhg9q4bw3H8wt\nj3bR8eTKRpdjZmY1OPT6wdnHT2bc8EEe7ZmZ7eEcev1gSFszHz3xYG5/fAV3PL6i0eWYmVkVDr1+\nctZxk9hv5CAuunEREdHocszMrAcOvX4yuLWZOScdwvwnV3HrYy80uhwzM+uBQ68fnXnsRMaPHsI3\nb3zUoz0zsz2QQ68fDWpp5mNvOYT7l67m5kXLG12OmZlVyDX0JM2QtEjSYknn9/D4YZLukPSSpE/n\nWctAeedrJzBp7FC++cdH2b7doz0zsz1JbqEnqRm4BDgZOBx4j6TDKxZbCXwc+EZedQy01uYm/uWt\nU1n4zFo++NP5rHxxc6NLMjOzVJ4jvenA4ohYEhGbgSuBmdkFImJ5RMwHtuRYx4A77ejxfGnmq7ht\n8QpO+c6t3P2Ev7RuZrYnyDP0xgNLM9Od6bxdJmm2pA5JHV1dXf1SXJ4kcfbxk7n6o69ncGsTsy67\ng4v/6zHv7jQza7C94kSWiLgsIqZFxLT29vZGl1O3I8aP4vqPv5FTjzyQb/zxUc654m661r3U6LLM\nzEorz9BbBkzMTE9I55XK8EEtfGfWa7jw9Fdz9xMrOeW7t3LbYn+Pz8ysEfIMvfnAVElTJLUBs4C5\nOb7eHksSs6ZP4ro5b2DUkFbe9+O7uOjGR9nm3Z1mZgMqt9CLiK3AHOAG4GHg1xGxUNJ5ks4DkLS/\npE7gk8DnJHVKGplXTY122P4jmTvnDbzzmAl896bHOOuHd/L82k2NLsvMrDS0t3UOmTZtWnR0dDS6\njN121T2d/Nt1DzK4tZmLzjyKE1+5b6NLMjPba0m6JyKm9bbcXnEiSxG987UTmDvnBPYdMYhzr5jP\nhb9/hBdf2trosszMCs0jvQbbtGUbX7r+IX5x19O0NInXTBzN8Qfvw/EH78Mxk8YwuLW50SWame3x\n6h3pOfT2EPOfXMnNjyzn9sdX8MCyNWzbHrS1NHHMpNG8/uBxHH/wPhw1YTRtLR6cm5lVcujtxdZt\n2sL8J1dyx+MruP3xFTz07FoiYEhrM9Mmj9kRgq/cbwSDW5uQ1OiSzcwayqFXIKs3bObOJSu5c8kK\nbn/8BR59fv2Ox9pamhg1pJXRQ1oZPbSVUUNaGTWkLZmXTu+c38rIIa2MGNzCyMGt3nVqZoVRb+i1\nDEQxtntGD21jxhH7M+OI/QHoWvcSdz2xgqdXbmDNxi2s2bCFNRu3sHrDFpat3sTDz65j9YbNvLh5\nW831trU0MXJwKyMHtzBiSPJz5JDWHfOGD2qhpbmJlibRnLm1NImm9Gd2XnNTE81N0KR0vpLlmpv0\nsnk715V8h7FJokkghAQS6byXTwt2zkNQ8Zgq1rHjfrq9SpcjXbZ7npmVh0NvL9Q+YhCnHnlgr8tt\n3rqdtZuSMFyzcTNrNm5h3aatrN24hbWbtrJ20xbWbtzKuk3p9MYtPLN64477L23dPgBbs+fYEYQ7\npneGaTI/DdrM8jtjNBH8/Z6TenamVGZv5Xq7w7tJO2uQdoa60j8cqAj6elXL/so6etPT9tdaZ+Xv\nPJnXtz9Eqm7DLq6uLzu/6vn99fTva+dylXfqVKXWejdBVSb64/2oVG2v4qH7jeD773ttv7xGPRx6\nBdbW0sS44YMYN3xQn56/Zdt2tm0Ptm4PtqW3rdu377j/d49tC7ZFcn9798/tlfPY+fwIIoII2B7B\n9mDHdJBMb++ejoppdv4n6n5+pPeDnc/p/n/W/Vhyf+fzuh/rnuj+b5ldT/b5Oz7UMzVUfij0+BFR\n63Mjak5mfic7t3/H/Exdye+vpzXUVu1DvtaHfxBVA7HWZ2R2nZXvQzKv99euVk+VB2o8p8bbsiuf\n83W8dPTw76tyub4eaqoWSr1tQk/1Vc7fxX9KNf9dVCtq0tihu/Yiu8mhZ1W1Njfhw35mViQ+/93M\nzErDoWdmZqXh0DMzs9Jw6JmZWWk49MzMrDQcemZmVhoOPTMzKw2HnpmZlcZe13BaUhfwVD+sahzw\nQj+sZ2/ibS6PMm63t7kcqm3zKyKivbcn73Wh118kddTTkbtIvM3lUcbt9jaXw+5us3dvmplZaTj0\nzMysNMocepc1uoAG8DaXRxm329tcDru1zaU9pmdmZuVT5pGemZmVjEPPzMxKo3ShJ2mGpEWSFks6\nv9H1DBRJT0p6QNJ9kjoaXU8eJF0uabmkBzPzxkq6UdJj6c8xjayxv1XZ5gskLUvf6/skndLIGvub\npImSbpb0kKSFkv45nV/Y97rGNhf9vR4s6W5J96fb/cV0fp/f61Id05PUDDwKvA3oBOYD74mIhxpa\n2ACQ9CQwLSIK+0VWSW8C1gM/i4gj0nlfA1ZGxIXpHzljIuKzjayzP1XZ5guA9RHxjUbWlhdJBwAH\nRMS9kkYA9wDvAM6loO91jW0+k2K/1wKGRcR6Sa3AX4F/Bk6nj+912UZ604HFEbEkIjYDVwIzG1yT\n9ZOIuAVYWTF7JvDT9P5PST4oCqPKNhdaRDwbEfem99cBDwPjKfB7XWObCy0S69PJ1vQW7MZ7XbbQ\nGw8szUx3UoJ/OKkA/iTpHkmzG13MANovIp5N7z8H7NfIYgbQxyQtSHd/FmY3XyVJk4GjgbsoyXtd\nsc1Q8PdaUrOk+4DlwI0RsVvvddlCr8xOiIjXACcD/zvdLVYqkezLL8P+/O8DBwGvAZ4FvtnYcvIh\naThwFfAvEbE2+1hR3+setrnw73VEbEs/uyYA0yUdUfH4Lr3XZQu9ZcDEzPSEdF7hRcSy9Ody4BqS\nXb1l8Hx6PKT7uMjyBteTu4h4Pv2g2A78kAK+1+nxnauAn0fE1ensQr/XPW1zGd7rbhGxGrgZmMFu\nvNdlC735wFRJUyS1AbOAuQ2uKXeShqUHv5E0DHg78GDtZxXGXOCc9P45wHUNrGVAdH8YpE6jYO91\nenLDj4GHI+KizEOFfa+rbXMJ3ut2SaPT+0NITkJ8hN14r0t19iZAekrvt4Fm4PKI+EqDS8qdpINI\nRncALcAvirjdkn4JnEhy6ZHngS8A1wK/BiaRXJLqzIgozIkfVbb5RJLdXQE8CXw4c/xjryfpBOBW\n4AFgezr7X0mOcRXyva6xze+h2O/1kSQnqjSTDNJ+HRFfkrQPfXyvSxd6ZmZWXmXbvWlmZiXm0DMz\ns9Jw6JmZWWk49MzMrDQcemZmVhoOPTNA0u3pz8mSzurndf9rT6+VF0nvkPT5XpZ5V9q1frukaTWW\nOyftZP+YpHMy86dIukvJ1Up+lX7vFSW+m85fIOmYdH6bpFsktfTXdpr1hUPPDIiI16d3JwO7FHp1\nfJC/LPQyr5WXzwDf62WZB0k61d9SbQFJY0m+93ccSaePL2R6O34V+FZEHAKsAj6Yzj8ZmJreZpO0\nySJt8H4T8O4+bI9Zv3HomQGSuju5Xwi8Mb022SfSZrdflzQ/Hbl8OF3+REm3SpoLPJTOuzZt6L2w\nu6m3pAuBIen6fp59rXRU9HVJDyq51uG7M+v+s6TfSnpE0s/TjhxIulDJNdUWSPq7y8lIOhR4qfsS\nUpKuk3R2ev/D3TVExMMRsaiXX8s/kjT4XRkRq4AbgRlpLW8Bfpsul+1yP5PkMkcREXcCozNdQ64F\n3tv7u2GWH+9qMHu584FPR8SpAGl4rYmIYyUNAm6T9Md02WOAIyLiiXT6AxGxMm2XNF/SVRFxvqQ5\nacPcSqeTdNM4iqSjynxJ3SOvo4FXAc8AtwFvkPQwSaupwyIiutszVXgDcG9menZa8xPAp4DX7cLv\notpVSfYBVkfE1or5tZ7zLMno8thdeH2zfueRnlltbwfOTi9tchfJB/7U9LG7M4EH8HFJ9wN3kjQ2\nn0ptJwC/TBsGPw/8hZ2hcHdEdKaNhO8j2e26BtgE/FjS6cCGHtZ5ANDVPZGu9/MkjXo/1ci2XBGx\nDdjc3QfWrBEcema1CfhYRLwmvU2JiO6R3os7FpJOBN4KHB8RRwF/Awbvxuu+lLm/DWhJR1bTSXYr\nngr8oYfnbezhdV8NrAAO3MUaql2VZAXJbsuWivm1ntNtEElwmzWEQ8/s5dYB2ZHIDcBH0su6IOnQ\n9EoVlUYBqyJig6TDePluxC3dz69wK/Du9LhhO/Am4O5qhSm5ltqoiJgHfIJkt2ilh4FDMs+ZTnJy\nydHApyVNqbb+dPnxkm5KJ28A3i5pTHoCy9uBG9Lrl90MnJEul+1yP5dkZCxJryPZNfxsuu59gBci\nYkutGszy5NAze7kFwDZJ90v6BPAjkhNV7pX0IPADej4W/gegJT3udiHJLs5ulwELuk8iybgmfb37\ngf8CPhMRz9WobQRwvaQFwF+BT/awzC3A0WnoDCK5xtoHIuIZkmN6l6ePnSapEzge+J2kG9LnHwBs\nBUh3hX6Z5JJc84EvZXaPfhb4pKTFJLt8f5zOnwcsARanr/3RTG0nAb+rsX1mufNVFswKRtJ3gP+M\niD/14blvVxl+AAAAWElEQVRzgKcjot+vMynpauD8iHi0v9dtVi+HnlnBSNoPOC6P4Oqr9MvrsyLi\nZ42uxcrNoWdmZqXhY3pmZlYaDj0zMysNh56ZmZWGQ8/MzErDoWdmZqXx/wFkjyiNNbzzCAAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110671470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "On the train set:\n",
      "Accuracy: 0.928909952607\n",
      "On the test set:\n",
      "Accuracy: 0.95\n"
     ]
    }
   ],
   "source": [
    "parameters = model(train_X, train_Y, keep_prob = 0.86, learning_rate = 0.3)\n",
    "\n",
    "print (\"On the train set:\")\n",
    "predictions_train = predict(train_X, train_Y, parameters)\n",
    "print (\"On the test set:\")\n",
    "predictions_test = predict(test_X, test_Y, parameters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:34:29.574182Z",
     "start_time": "2018-01-20T00:34:29.569461Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20, 2)\n"
     ]
    }
   ],
   "source": [
    "print(parameters['W1'].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dropout works great! The test accuracy has increased again (to 95%)! Your model is not overfitting the training set and does a great job on the test set. The French football team will be forever grateful to you! \n",
    "\n",
    "Run the code below to plot the decision boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-20T00:33:34.997243Z",
     "start_time": "2018-01-20T00:33:34.645069Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GhCvVCMZed+0ldG3WbxRGls9INNri7yCi8UzzYEJRshF3DxHdf6eNK7lDk4Uc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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f7bdcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Model with dropout\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-0.75,0.40])\n",
    "axes.set_ylim([-0.75,0.65])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Note**:\n",
    "- A **common mistake** when using dropout is to use it both in training and testing. You should use dropout (randomly eliminate nodes) only in training. \n",
    "- Deep learning frameworks like [tensorflow](https://www.tensorflow.org/api_docs/python/tf/nn/dropout), [PaddlePaddle](http://doc.paddlepaddle.org/release_doc/0.9.0/doc/ui/api/trainer_config_helpers/attrs.html), [keras](https://keras.io/layers/core/#dropout) or [caffe](http://caffe.berkeleyvision.org/tutorial/layers/dropout.html) come with a dropout layer implementation. Don't stress - you will soon learn some of these frameworks.\n",
    "\n",
    "<font color='blue'>\n",
    "**What you should remember about dropout:**\n",
    "- Dropout is a regularization technique.\n",
    "- You only use dropout during training. Don't use dropout (randomly eliminate nodes) during test time.\n",
    "- Apply dropout both during forward and backward propagation.\n",
    "- During training time, divide each dropout layer by keep_prob to keep the same expected value for the activations. For example, if keep_prob is 0.5, then we will on average shut down half the nodes, so the output will be scaled by 0.5 since only the remaining half are contributing to the solution. Dividing by 0.5 is equivalent to multiplying by 2. Hence, the output now has the same expected value. You can check that this works even when keep_prob is other values than 0.5.  "
   ]
  },
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   "source": [
    "## 4 - Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Here are the results of our three models**: \n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "        <td>\n",
    "        **model**\n",
    "        </td>\n",
    "        <td>\n",
    "        **train accuracy**\n",
    "        </td>\n",
    "        <td>\n",
    "        **test accuracy**\n",
    "        </td>\n",
    "\n",
    "    </tr>\n",
    "        <td>\n",
    "        3-layer NN without regularization\n",
    "        </td>\n",
    "        <td>\n",
    "        95%\n",
    "        </td>\n",
    "        <td>\n",
    "        91.5%\n",
    "        </td>\n",
    "    <tr>\n",
    "        <td>\n",
    "        3-layer NN with L2-regularization\n",
    "        </td>\n",
    "        <td>\n",
    "        94%\n",
    "        </td>\n",
    "        <td>\n",
    "        93%\n",
    "        </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>\n",
    "        3-layer NN with dropout\n",
    "        </td>\n",
    "        <td>\n",
    "        93%\n",
    "        </td>\n",
    "        <td>\n",
    "        95%\n",
    "        </td>\n",
    "    </tr>\n",
    "</table> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that regularization hurts training set performance! This is because it limits the ability of the network to overfit to the training set. But since it ultimately gives better test accuracy, it is helping your system. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Congratulations for finishing this assignment! And also for revolutionizing French football. :-) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<font color='blue'>\n",
    "**What we want you to remember from this notebook**:\n",
    "- Regularization will help you reduce overfitting.\n",
    "- Regularization will drive your weights to lower values.\n",
    "- L2 regularization and Dropout are two very effective regularization techniques."
   ]
  }
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